Algebra and Trigonometry (6th Edition)

Chapter 9

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; Isolate on one side of the second equation of ... more

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; Multiply the second equation by 2. ; Subtract ... more

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; Rewrite both equations in the given system in ... more

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; The given system of equations will be solved by... more

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   ; The first equation of the given system is ... more

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100 ounces of solution60 ounces of solution ; ... more

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Satisfies both equations in the given system ; ... more

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The point of intersection of the two lines ; A ... more

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; Substitute the value of into the second ... more

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; The coefficients of the variable in the first ... more

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; Multiply the first equation by 2.Multiply the ... more

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; Since is a false statement, then the given ... more

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or ; Since is a true statement, the given system ... more

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Revenue ; The revenue function, , gives the amount... more

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Break-even point ; If units of the product sold ... more

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The ordered pair is a solution of the system. ; ... more

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The ordered pair is a solution of the system. ; ... more

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The ordered pair is not a solution of the system... more

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The ordered pair is not a solution of the system... more

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; The second equation already expresses in terms... more

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; The second equation already expresses in terms... more

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; The second equation already expresses in terms... more

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; The second equation already expresses in terms... more

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; The first equation already expresses in terms ... more

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; The first equation already expresses in terms ... more

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; For the second equation of the given system, ... more

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; For the second equation of the given system, ... more

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; Given the second equation of the system:... more

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; Given the second equation of the system:... more

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; Rewrite both equations in the given system in ... more

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; Rewrite both equations in the given system in ... more

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; The first equation already expresses in terms ... more

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; The first equation already expresses in terms ... more

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; Add the two equations. ; Divide both sides of ... more

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; Add the two equations. ; Divide both sides of ... more

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; Add the two equations. ; Divide both sides of ... more

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; Add the two equations. ; Divide both sides of ... more

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; Multiply both sides of the first equation by 4... more

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; Multiply both sides of the second equation by 7... more

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; Multiply both sides of the second equation by –... more

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; Multiply both sides of the first equation by... more

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; Multiply both sides of the first equation by , ... more

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; Multiply both sides of the first equation by 5... more

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; Rewrite each equation in the form . ; Multiply ... more

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; Rewrite each equation in the form . ; Multiply ... more

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; Substitute the value of from the first ... more

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; Substitute the value of from the second ... more

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; Substitute the value of from the first ... more

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; Substitute the value of from the second ... more

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; Multiply both sides of the second equation by 2... more

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; Multiply both sides of the second equation by 5... more

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; Multiply both sides of the first equation by... more

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; Multiply both sides of the second equation by... more

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; Multiply both sides of the first equation by... more

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; Multiply both sides of the first equation by... more

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; Rewrite each equation in the form . ; Multiply ... more

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; Rewrite each equation in the form . ; Multiply ... more

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; ; and ; Rewrite the mathematical sentences into... more

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; ; and ; Rewrite the mathematical sentences into... more

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; ; and ; Rewrite the mathematical sentences into... more

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; ; and ; Rewrite the mathematical sentences into... more

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; To eliminate the denominator, multiply both ... more

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; To eliminate the denominator, multiply both ... more

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; Multiply both sides of the second equation by... more

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; Multiply both sides of the first equation by , ... more

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; ; Write an equation by substituting 11 for the ... more

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; ; Write an equation by substituting 23 for the ... more

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; ; Determine the linear equations which pass ... more

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; ; Determine the linear equations which did not ... more

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; Substitute for and . ;   ; Multiply both ... more

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; From the graph, determine the values of such ... more

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; there is a loss of when 200 devices are made ... more

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; there is a loss of when 300 devices are made ... more

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are engaged in online gaming at least once per day... more

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sleeps from 5 to 7 hourssleeps from 9 to 11 hours... more

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6 ounces ; Let and be the weight (in ounces) of... more

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160 ounces ; Let and be the weight (in ounces) ... more

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600 learners from NC400 learners from SC ; Let ... more

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750 learners from NC450 learners from SC ; Let ... more

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50 rooms with kitchenettes150 non-kitchenette ... more

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6 two-seater dining tables11 four-seater dining ... more

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speed in calm water: 6 mphcurrent’s speed: 2 mph... more

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rate in tranquil air: 180 mphwind’s speed: 20 mph... more

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; The sum of the measures of the three interior ... more

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; The sum of the degree measures of the three ... more

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A set of two linear equations, usually of the form... more

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Any ordered pair that satisfies both equations in... more

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Solve either equation for one of the variables in ... more

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Start by multiplying either one or both of the ... more

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When the coefficients of either variable ( or ) ... more

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A system of equations has infinite number of ... more

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A system of linear equations has no solution, if ... more

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The break-even point is the point where the ... more

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E5 ; E6 ; E7 ; E8 ; E11 ; Use a graphing utility ... more

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The statement makes sense. Fractions lie between ... more

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The statement makes sense. Linear equations are ... more

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The statement does not make sense. Systems of ... more

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The statement makes sense. The values of and can... more

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  ; Consider the linear system. In the second ... more

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; Solve the system using the addition method.... more

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The liar twin gave the problem.  ; Let and be ... more

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katex in solution acts like image, cannot be ... more

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Yes. 8 six-sided and 4 four-sided formations can ... more

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; The given function is a natural logarithmic ... more

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If the vehicle is 12 feet wide, its edges ... more

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; Condense the logarithm by applying the product ... more

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Amplitude: 2Period: Phase shift: ; To graph a ... more

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 is a solution of the equation. ; Substituting... more

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; Multiply the second equation by 2. ; Add the ... more

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; Substituting and in the given equation yields... more

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Substitute the ordered triple in the given ... more

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; Add equation 1 and equation 2 to get an ... more

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; Multiply equation 2 by 2, and subtract equation... more

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; The graph must pass through the given points so... more

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triple ; The triple is a set of three real numbers... more

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-2-4 ; Multiply equation 1 by -2, so that on ... more

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add equation 1 and 3 ; The term is missing from ... more

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Yes ; The given triple is solution of the system ... more

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Yes ; The given triple is solution of the system ... more

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Yes ; The given triple is solution of the system ... more

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Yes. ; The given triple is solution of the system ... more

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; Multiply equation 1 by -1, and add it to ... more

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; Multiply equation 1 by 3, and add it to ... more

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; Multiply equation 1 by 2, and add it to the ... more

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; Add equation 1 and equation 2 to get an ... more

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; Multiply equation 1 by 2 and equation 2 by -3, ... more

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; Multiply equation 1 by 2 and equation 2 by -3, ... more

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; Multiply equation 2 by 2, and add it to the ... more

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; Multiply equation 3 by 2, and add it to the ... more

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; Add equation 2 and equation 3 to get an ... more

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; Multiply equation 1 by -3, and add it to the ... more

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; Multiply equation 2 by 3, and add it to the ... more

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; Multiply equation 1 by -1, and add it to the ... more

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; Simplify each of the 3 given equations in the ... more

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; Simplify each of the 3 given equations in the ... more

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; The graph must pass through the given points so... more

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; The graph must pass through the given points so... more

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; The graph must pass through the given points so... more

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; The graph must pass through the given points so... more

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; TLet the three numbers be and . Form three ... more

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; Let the three numbers be and .Form three ... more

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, and ; Convert the given equations to standard ... more

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; Convert the given equations to standard form by... more

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; Use the points and to find the three ... more

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; Use the points and to find the three ... more

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; Add equation 1 and equation 2 to get an ... more

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; Add equation 1 and equation 3 to get an ... more

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. ; Construct the equations from the given ... more

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; Construct the equations from the given ... more

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; Let us assume that a gallon of Product M costs... more

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; Let us assume that a gallon of Product M costs... more

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; Let the number of tickets of each type be , and... more

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; Let the packages of Product B of each type be... more

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; Let the amount invested at each rate be , and... more

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; Let the amount invested at each rate be , and... more

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; The sum of the interior angles of a triangle is... more

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; A linear equation is one in which the power of ... more

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The ordered triple must satisfy the equations such... more

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Use elimination, addition, and multiplication to ... more

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Use a system of linear equations in three unknowns... more

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Yes 5.2.5. 5.2.7. 5.2.9. 5.2.11. 5.2.13. ; A ... more

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  For Exercise 19 ; For Exercise 20 ; For Exercise... more

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The statement doesn't make sense. ; The value of ... more

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The statement does not make sense. ; The system of... more

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Yes, the statement does make sense. ; The equation... more

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The statement does make sense. ; The population ... more

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The system of given equations can be solved by ... more

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triangles, rectangles, pentagons. ; Let and, ... more

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line graph: curve graph: ; Derive a function for ... more

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; Find the Lowest Common Multiple (L.C.M) on both... more

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; Arrange the equation into the form of . ; Here... more

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; Let be an angle within the interval whose sine ... more

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; Find the Least Common Denominator (L.C.D.) of ... more

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; Find the Least Common Denominator (L.C.D.) of ... more

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; Multiply equation 1 by 2, and add it to ... more

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; The denominator consists of two linear factors ... more

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; The denominator consists of a linear factor and... more

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; The denominator consists of a linear and a ... more

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; The denominator is of the form of repeated ... more

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Correct ; The denominator consists of product of ... more

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Incorrect ; The decomposition for the repeated ... more

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Incorrect ; is a quadratic factor that can't be ... more

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Correct ; The denominator is a repeated quadratic ... more

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; The denominator is the product of two linear ... more

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; The denominator is the product of two linear ... more

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; The denominator consists of a linear factor ... more

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; The denominator consists of a linear factor ... more

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; There are two factors in the denominator. is a... more

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; There are two factors in the denominator. is a... more

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; The denominator has a quadratic factor raised ... more

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; The denominator has a quadratic factor raised ... more

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; The denominator consists of two linear factors ... more

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; The denominator consists of two linear factors ... more

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; The denominator consists of two linear factors ... more

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; The denominator consists of two linear factors ... more

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; The denominator consists of a single quadratic ... more

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; The denominator consists of a single quadratic ... more

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; The denominator consists of a single quadratic ... more

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; The denominator consists of a single quadratic ... more

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; The denominator consists of three linear ... more

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; The denominator consists of three linear ... more

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; Simplify the denominator and write it in the ... more

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; Simplify the denominator and write it in the ... more

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; The denominator consists of a repeated linear ... more

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; The denominator consists of a repeated linear ... more

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; The denominator consists of a repeated linear ... more

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; The denominator consists of a repeated linear ... more

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; The denominator consists of a linear factor and... more

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; The denominator consists of a linear factor and... more

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; The denominator consists of a linear factor and... more

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; The denominator consists of two repeated linear... more

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; The denominator consists of a linear factor and... more

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; The denominator consists of a linear factor and... more

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; The denominator consists of a linear factor and... more

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; The denominator consists of a linear factor and... more

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; The denominator consists of a repeated linear ... more

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; The denominator consists of a repeated linear ... more

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; Factor the denominator. The denominator ... more

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; Factor the denominator. The denominator ... more

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; The denominator is a repeated quadratic factor... more

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; The denominator is a repeated quadratic factor... more

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; The denominator is a repeated quadratic factor.... more

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; The denominator is a repeated quadratic factor... more

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; Factor the denominator using the identity. The ... more

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; Factor the denominator using the identity .The ... more

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; The given fraction is an improper fraction. ... more

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; The given fraction is an improper fraction. ... more

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; The given fraction is an improper fraction. ... more

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; The given fraction is an improper fraction. ... more

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; Factor the denominator of the given fraction... more

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; Factor the denominator of the given fraction... more

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; The denominator is a repeated linear factor. ... more

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; Factor the denominator.  ; The denominator now ... more

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; The denominator consists of two linear factors... more

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; The denominator consists of two linear factors... more

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The partial fraction decomposition is the breaking... more

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The partial fraction decomposition of distinct ... more

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The partial fraction decomposition of repeated ... more

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The partial fraction decomposition of the ... more

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The partial fraction decomposition of repeated ... more

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The verification of partial fraction decomposition... more

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The decompositions are verified with the rational ... more

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The statement doesn’t make sense because a single ... more

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The statement doesn’t make sense because the ... more

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The statement makes sense since the linear factor ... more

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The statement doesn’t make sense as writing down ... more

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The denominator with a cubic factor raised to ... more

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; Factor the denominator of the given fraction... more

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; Use the fact that and rewrite the given ... more

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Yes ; Subtract on both sides to get the equation ... more

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; Solve for using the fact that the sum of the ... more

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; Let the given equations be equation 1 and ... more

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; Let the given equations be equation 1 and ... more

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From the graph, the points of intersection are ... more

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; From equation two, solve for in terms of .Add... more

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; From equation one, solve for in terms of . ... more

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; Choose a variable to eliminate. Multiply an ... more

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; Subtract from both sides. ; Add the equations ... more

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7 feet by 3 feet ; Let be the length and the ... more

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Nonlinear equation ; A linear equation has a ... more

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; Find the values of to obtain the solution set ... more

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0355HP ; To eliminate a variable by addition, its ... more

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; Find the values of by taking the square root ... more

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; To eliminate a variable by addition, its ... more

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; Solve for in terms of by dividing both sides ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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; From equation two, solve for in terms of . ; ... more

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; From equation two, solve for in terms of . ; ... more

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; From equation two, solve for in terms of . ; ... more

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; From equation two, solve for in terms of . ; ... more

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; From equation two, solve for in terms of . ; ... more

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; From equation two, solve for in terms of . ; ... more

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; From equation one, solve for in terms of . ; ... more

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; From equation one, solve for in terms of . ; ... more

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; From equation one, solve for in terms of . ; ... more

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; From equation one, solve for in terms of . ; ... more

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; From equation one, solve for in terms of . ; ... more

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; From equation one, solve for in terms of . ; ... more

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; Add the equations to eliminate .  ; Solve the ... more

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; Add the equations to eliminate .  ; Solve the ... more

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; Eliminate . Multiply equation two by 4, then ... more

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; Eliminate . Multiply equation two by , then add... more

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; Write the equations in the form . ; Eliminate... more

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; Write the equations in the form . ; Eliminate... more

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; Write the equations in the form . ; Eliminate... more

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; Obtain an equation in one variable by ... more

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; Align similar terms. ; Obtain an equation in ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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; From equation 2, solve for in terms of . ... more

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; From equation 2, solve for in terms of . ... more

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; From equation 2, solve for in terms of . ; ... more

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; From equation 2, solve for in terms of . Add ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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; From equation 2, solve for in terms of . ; ... more

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; From equation 2, solve for in terms of . ; ... more

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; From equation 1, solve for in terms of . ; ... more

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4 and 6 ; Write the equations. ; Solve the system ... more

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8 and 12 ; Write the equations. ; Solve the system... more

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; Write the equations. ; Obtain an equation in ... more

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; Write the equations. ; Obtain an equation in ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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; Obtain an equation in one variable by ... more

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Graph and .Press Y=.Input into Y1 and into Y2.... more

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; The solution of the system is , which is the ... more

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; To find the intersection of the two space ... more

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; Find the intersection of the two equations. ... more

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11 feet by 7 feet ; Let be the length and the ... more

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12 feet by 8 feet ; Let be the length and the ... more

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8 inches by 6 inches ; Let be the length and be ... more

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12 feet by 9 feet ; Let be the length and be the... more

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5 meters; 2 meters ; Let be the side length of ... more

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14 feet by 8 feet  ; Let be the length and be ... more

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A nonlinear system is a system that involves an ... more

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From one equation, solve for one variable in terms... more

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Align similar terms.Make the coefficients of the ... more

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5.4.1. ; 5.4.3. ; 5.4.5. ; 5.4.7. ; 5.4.9. ; 5.4.1... more

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; Graph and .Press Y=.Input into Y1 and into ... more

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To eliminate a variable in a linear system or a ... more

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The statement does make sense. ; Planet E ... more

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The statement makes sense. ; The graph of both ... more

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The statement does not make sense. ; A graphical ... more

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False; two real-ordered pair solutions. ; The ... more

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True. ; It is possible for a circle, which is ... more

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The statement is false. A system of two equations ... more

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This statement is false.  A system of two ... more

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18 sq. units ; Using the first equation, isolate ... more

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; ; Write equations using the Pythagorean theorem... more

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; Rewrite each equation in exponential form... more

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; Rewrite each equation in exponential form... more

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; Determine the possible rational roots.  ; ... more

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; Let and be positive real numbers. Use the ... more

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Let be the integers from to 3. Substitute each ... more

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Substitute into . ; Let be the integers from to... more

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Substitute into . ; Let be the integers from to... more

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; Substitute the value of from the first ... more

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; Multiply both sides of the first equation by 2 ... more

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; To eliminate the denominators, multiply each ... more

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; ; Substitute the value of from the first ... more

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; To eliminate the terms with , multiply both ... more

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; To eliminate the denominator, multiply both ... more

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; To obtain a fourth equation, multiply the first... more

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; To obtain a fourth equation, multiply the ... more

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; Isolate the variable by subtracting and ... more

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; Multiply both sides of the second equation by 2... more

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; Substitute the value of from the first ... more

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; Isolate the value of by adding to both sides ... more

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; Rewrite the equation using partial fractions ... more

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; Factor the denominator. Then, rewrite the ... more

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; Rewrite the equation using partial fractions ... more

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; Rewrite the equation using partial fractions ... more

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gallons; gallons ; Equate the sum of mixture and... more

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; Equate the sum of , , and to 180. Note that ... more

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; Write three equations by substituting the value... more

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, ; The sum of the two lengths, , and two widths... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Any point that is a solution to all the ... more

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The overlapping area is the region of solution for... more

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The solution is the shaded region common to both ... more

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The solution is the shaded region common to all ... more

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solution; ; ; ; Any ordered pair that results in ... more

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Graph ; A linear inequality has infinite solutions... more

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half-plane ; When a linear inequality is graphed, ... more

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The graph will not include the line as the line ... more

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To find the solutions to a linear inequality, the ... more

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To find the solutions to a linear inequality the ... more

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; The equation corresponding to the inequality ... more

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; The system is comprised of two inequalities and... more

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The intersection point of the two inequalities ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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Replace the inequality symbol with the equality ... more

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